We measure the Kerr-nonlinear index of refraction of a three-level Lambda-type atomic system inside an optical ring cavity. The Kerr nonlinearity is modified and greatly enhanced near atomic resonant conditions for both probe and coupling beams. The Kerr nonlinear coefficient n(2) changes sign when the coupling beam frequency detuning switches sign, which can lead to interesting applications in...

Several necessary and suucient conditions for the pseudometric generating property of non-additive set functions are given. The relation among the pseudometric generating property and autocontinuity of fuzzy measures is depicted by using the absolute continuity and exhaustivity. Moreover, any uniformly autocontinuous nite fuzzy measure is equivalent to a subadditive nite fuzzy measure. A furthe...

The transverse velocity distribution of a sodium atomic beam, laser cooled in one dimension, has been measured with sub-recoil resolution. A velocity-selective detection system was employed to separate the longitudinal and transverse velocity components to provide a direct measure of the transverse velocity distribution. The effects of varying the cooling laser intensity and detuning on the der...

A quantitative measure is proposed to evaluate and optimize the design of quantitative atomic resolution TEM experiments. It aims at precise measurement of unknown structure parameters. Specifically, the proposed measure quantifies the statistical precision with which positions of atom columns can be estimated. The optimal design is then given by the combination of microscope settings for which...

If Ill' ... , ~tn are non-atomic probability measures on the same measurable space (S, ff"), then there is an ff"-measurable partition {AJ7= 1 of S so that IlJAi)~(n-l+m)-l for all i=I, ... ,n, where m=l l i 01 lli l l is the total mass of the largest measure dominated by each of the Il/s; moreover, this bound is attained for all n ~ 1 and all m in [0,1]. This result is an analog of the bound (...

MOTIVATION Geometric representations of proteins and ligands, including atom volumes, atom-atom contacts and solvent accessible surfaces, can be used to characterize interactions between and within proteins, ligands and solvent. Voronoi algorithms permit quantification of these properties by dividing structures into cells with a one-to-one correspondence with constituent atoms. As there is no g...

Mapping atomic displacement at the nanoscale is crucial for developing and optimizing strain-engineered devices. In today’s transistors, a slight deformation of the silicon lattice in the source-drain regions enhances their performance. And in the future, strain-induced electro-optic effects may potentially form the basis of an all-silicon electronic and photonic device. Transmission electron m...